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A mathematical model for diagnosing the state of solid insulation of high-voltage transformers based on an informational assessment of indirect indicators, i.e. entropy, for example, by the content of impurities of various gases dissolved in transformer oil, which allows to determine the technical condition without removing the workload. The values of the average information on the working and faulty state of insulation for various types of gas impurities are calculated.

In connection with the negative effects caused by the fault of the insulators used in an overhead power transmission line of 6 - 10 kV, it is suggested controlling a condition of a post insulator by the device that responses when breakdown current goes through an insulator. The work of the device for identification of insulators defects is described. Equivalent circuits of an alarm device connection with an insulator in an overhead power transmission line are given. The basic processes, that occur in a system of a supporting insulator of an overhead power transmission line in a serviceable condition and if there is a defect in view of geometric capacitance, absorption current, steady leakage current and surface current of breakdown, are considered.

Now there is no efficient decision to estimate a corrosion condition of an underground part of reinforced concrete support of contact network which is not demanding digging of a support. This problem makes actual a task of development of a hardware and software system of definition of a corrosion condition of an underground part of reinforced concrete support of contact network. As a result of work the software module allowing to realize panoramic shooting of an internal surface of an underground part of a support, to increase quality of the received images, to carry out searching of inhomogeneities and to determine their geometrical parameters, and also to make the analysis of the found inhomogeneities. Implementation of results of work will allow to reduce time and labor costs, and also to increase efficiency of diagnostic works on support of contact network.

The article describes a software module of the initial image processing which allows to perform the contour image analysis in order to find, recognize and evaluate graphic images of various types of inhomogeneities. Application of software module will improve the accuracy of the evaluation of the internal surface of closed vessels in the absence of access control.

The method of an estimation of reliability of functioning and probability of conditional non-failure operation of a network element telecommunication in view of factor of availability is considered

The article examines the technique of designing diagnostic system of infrastructure of electrical railways based on use of bayesian networks for prediction of probabilities of failures. To achieve maximum effectiveness of diagnosis we should minimize the number of input parameters, while maintaining the required accuracy. It is proposed to create a mathematical model of the diagnostic system, that will allow to evaluate the influence of each parameter on the accuracy of prediction of failures. To compensate the lack of source data we can use the advantage of bayesian networks - the opportunity to generate network structure by the method of expert evaluations. Generated bayesian network will perform the failure probability calculation with limited information.

The article presents the results of research of a point magneto-induction sensor based on a mathematical model, which allows you to increase the reliability of automated systems for diagnosing technical condition rolling stock in the course of train movement by improvement the accuracy of the initial information, that is, the moments of fixation passing of wheelset axles over magneto-induction sensors. At the first stage of developing a stigmatic mathematical model the analytical dependence of the value of the magnetic flux in the magnetic core and the output EMF value on resistance of the air gap between the sensor and the wheel crest. At the second stage of development of the mathematical model found time dependence of the magnetic resistance of the air gap between the core of the magneto-induction sensor and the comb wheels of a railway car moving along a straight track at a constant speed. On the basis of application the developed stigmatic model allows evaluating the energy parameters of magneto-induction sensors depending on the properties of modern magnetic materials. The simulation results showed that the MMF value is constant the magnet determines the main parameters of magneto-induction sensors, so the use of modern magnets based on rare earth they allow to eliminate the traditional disadvantage of outdated types of magneto-induction sensors, that is, to reduce their size and weight. The application of the proposed stigmatic model expands the scope of possible solutions to extreme problems for selection and justification parameters of magneto-induction sensors, helps to improve the accuracy of systems for diagnosing the technical condition of the car fleet and traffic safety on railway transport.